Countable Subgroups of Homeomorphism Groups: Dimension One and Beyond - Lecture 2

Explore countable subgroups of homeomorphism groups in this 51-minute lecture from the Orderable Groups conference. Delve into problems concerning finitely generated and countable subgroups with specific properties, focusing on regularity in dimension one. Examine aspects of joint work with S. Kim on critical regularity and discover the outline of a program to generalize one-dimensional results to higher dimensions. Learn about recent findings in the model theory of homeomorphism groups of compact manifolds, developed in collaboration with S. Kim and J. de la Nuez Gonzalez. Gain insights into potential future generalizations of these concepts and their applications in mathematical research.